In a direct variation, the relationship between two variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is expressed by the equation [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.
Given the ordered pair [tex]\((4, 5)\)[/tex]:
- [tex]\( x = 4 \)[/tex]
- [tex]\( y = 5 \)[/tex]
First, we use the direct variation equation to find the constant of variation [tex]\( k \)[/tex]. We can solve for [tex]\( k \)[/tex] by rearranging the equation [tex]\( y = kx \)[/tex] to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{y}{x} \][/tex]
Next, substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ k = \frac{5}{4} \][/tex]
Therefore, the constant of variation [tex]\( k \)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
The correct statement is:
The constant of variation [tex]\( k \)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
